They might. In an edit above, I remarked that for such a system to exist indeed Project Treble is a necessity. But taking centralized control over the way Android updates will be a very ballsy political move by Google to make.
Some smaller vendors might appreciate that these responsibilities are taken away from them. Sony, HMD/Nokia and Lenovo/Motorola are basically only adding some apps, themes and tweaks to AOSP at this point anyway, but do tend to have relatively good update reputation (or used to). But other vendors will not appreciate giving away this control at all. Some vendors are likely partially motivated to not have devices updated in the first place.
So will Google make such a ballsy move? They themselves barely have good business reasons to do so. Android completely dominates the market anyway, without Google upsetting the politics amongst the vendors and pouring money into doing things that vendors refuse. It seems Android's bad reputation in regards to updates doesn't really hit anyone that hard.
Having said that, Project Treble does seem to be a move in that direction. Maybe Google cares enough about theirs and Android's reputation, or maybe they even care enough about being responsible. Maybe they'll make "Windows Update for Android" an opt-in thing for vendors. Maybe there are other ways they can create a more responsible market (and better repution for Android) without upsetting vendors. Let's hope they find a way at least.